Setting up Eclipse
Eclipse is an IDE originally designed for Java, but now with plugins for many languages, including PHP. It has lots of very powerful features, and it is the editor of choice for most of the OU Moodle developers, and a number of other people in the community.
However, it is not the easiest program in the world to get started with, so I'm going to take you through it step by step.
Eclipse is written in Java, so I would recommend getting the latest Java runtime environment from http://java.com/ for maximum speed and reliability.
Also, Eclipse is quite big, so I recomment lots of memory in your computer. I have used it on all of Windows, MacOS X and Linux with 1GB of memory, and that is plenty.
Go to http://www.eclipse.org/downloads/. Click on the link where it says Download now: Eclipse SDK 3.2 It should have automatically detected which platform you are using. Choose a Mirror, and wait for the ~100MB download.
You will notice that what you have got is a zip file (unless your system automatically decompresses it for you).
On Windows, upzip it into C:\Program Files (all the files go into an Eclipse folder there). Then look in the Eclipse folder and drag Eclipse.exe to the Start menu/Desktop/Quicklaunch bar to make a shortcut for starting it.
On MacOS, unzip and copy the Eclipse folder into Applications. Go into the Eclipse folder and drag the Eclipse app to the Dock for ease of launching.
On Linux, unzip somewhere suitable, and make an easy way to launch it.
The first time you run Eclipse
The first time you lauch Eclipse it does a bit of setup stuff, for instance, it create a workspace. This is where it stores the things you are working on. The default location is sensible on all platforms, so use that.
For some reason, every time you start Eclipse, it asks you which workspace you want to use. I have never seen the need to have more than one, so I recommend turning on the checkbox that says "Don't ask me this again".
Another thing that happens the first time you run Eclipse is that you arrive at a welcome screen. This has links to various bits of help, which you can read if you like, but you probaly don't need to if you are following these instructions. So find the button on the welcome page that closes it and gets you to the main Eclipse screen.